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Table 7 Problem 3 : MAEs using ( 2.21a )-( 2.21b ) with \(\pmb{C=\sqrt{\lambda}}\) for \(\pmb{0< x<\frac{1}{2}}\) and \(\pmb{C=\frac {1}{\sqrt{\lambda}}}\) for \(\pmb{\frac{1}{2} \leq x <1}\)

From: A class of quasi-variable mesh methods based on off-step discretization for the solution of non-linear fourth order ordinary differential equations with Dirichlet and Neumann boundary conditions

λ \(\boldsymbol {10^{2}} \) \(\boldsymbol {10^{4}} \) \(\boldsymbol {10^{6}} \) \(\boldsymbol {10^{8}} \)
N u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\) u \(\boldsymbol {u'}\)
32 3.08e−05 1.71e−04 1.11e−04 2.84e−03 5.24e−05 1.24e−02 1.25e−05 3.01e−02
64 3.96e−06 2.10e−05 8.40e−06 2.29e−04 4.06e−06 9.84e−04 1.22e−06 2.89e−03
128 5.28e−07 2.69e−06 7.38e−07 2.15e−05 3.18e−07 8.45e−05 9.06e−08 2.32e−04
256 6.91e−08 3.43e−07 7.49e−08 2.31e−06 2.91e−08 8.39e−06 7.76e−09 2.16e−05
Order 2.93 2.97 3.30 3.22 3.45 3.33 3.55 3.43